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+\documentclass[a4paper]{article}
+
+\usepackage{pgfplots}
+
+\pgfplotsset{compat=newest}
+
+\begin{document}
+
+\begin{tikzpicture}
+ \begin{axis}[
+ point meta rel=per plot,
+ filter discard warning=false,
+ ]
+ \addplot3[surf,domain=0:1] {
+ x+y
+ + 0.8*sin(x*360)*x*(1-y)
+ + 0.4*(-sin(x*360)-sin(y*300))*(x+0.1)^2*(y+0.4)^2
+ + exp(-((x-0.2)^2 + (y-0.7)^2)*10)*0.8
+ };
+ \addplot3[red,
+ %--------------------------------------------------
+ % quiver={
+ % u=0,
+ % v=1,
+ % w=1-0.8*sin(1*360) ,
+ % },
+ %--------------------------------------------------
+ variable=\t,
+ domain=0:1,samples y=0]
+ (1.03,t,{
+ 1+t
+ + 0.8*sin(1*360)*1*(1-t)
+ + 0.4*(-sin(1*360)-sin(t*300))*(1+0.1)^2*(t+0.4)^2
+ + exp(-((1-0.2)^2 + (t-0.7)^2)*10)*0.8
+ });
+ %\tracingmacros=2 \tracingcommands=2
+ \addplot3[contour gnuplot={
+ number=9,
+ labels=false,
+ output point meta=rawz, % override the z filter
+ },
+ z filter/.code={%
+ \ifdim##1pt<0.15pt %
+ \def\pgfmathresult{}% skip incomplete contour
+ \else
+ \def\pgfmathresult{3}% fix complete contour plot at a specific level
+ \fi
+ },
+ domain=-0.3:0.6, domain y=-0.2:1.1,
+ colormap/hot,
+ ]
+ {
+ + exp(-((x-0.2)^2 + (y-0.7)^2)*10)*0.8
+ };
+
+ \addplot3[->,blue,domain=4:5*pi,variable=\t,samples=60,samples y=0]
+ ({sin(deg(t))*(1-t/5/pi)*0.3 + 0.2},
+ {cos(deg(t))*(1-t/5/pi)*0.15 + 0.7},
+ {3*t/(5*pi)});
+
+ \addplot3[quiver={
+ % deg'(t) !?
+ u= cos(deg(t)) * (1-t/5/pi)*0.3 - sin(deg(t)) *0.3 /5/pi,
+ v=-sin(deg(t)) * (1-t/5/pi)*0.15- cos(deg(t)) *0.15/5/pi,
+ w=3/5/pi,
+ scale arrows=1.5,
+ },
+ red,
+ -stealth,
+ variable=\t,
+ domain=4:5*pi,samples=5,samples y=0]
+ ({sin(deg(t))*(1-t/5/pi)*0.3 + 0.2},
+ {cos(deg(t))*(1-t/5/pi)*0.15 + 0.7},
+ {3*t/(5*pi)});
+ \end{axis}
+\end{tikzpicture}
+\end{document}
+